Blender stops responding when trying to export fbx with empties but doesn't with just one empty
Seeing the same result you are, taking a very long time to process

My blind guess is that if you wait long enough it will eventually export the file successfully, since selecting only a subset of the empties exported successfully after a while, although it may take longer than you are willing to wait.

The resulting (partial) file did however have 200+ Mb in size, so something else other than geometry is being processed and exported that is causing the long delays and large file size.

I noticed that some objects did have some animations in them, so that must be causing the delay and file bloat. Disabling animation export in the FBX dialog resulted in a 500kb file that exported in seconds.

This may be an actual bug or a result of the high number of empties, heavy use of parent relationships, baking of animations, or any combination of both.